3 papers
math.DS2025
Equidistribution of nilflows and bounds on Weyl sums
Livio Flaminio, Giovanni Forni
We prove an effective equidistribution result for a class of higher step nilflows, called filiform nilflows, and derive bounds on Weyl sums for higher degree polynomials with a pow…
math.DS2024
On rigidity properties of time-changes of unipotent flows
Mauro Artigiani, Livio Flaminio, Davide Ravotti
We study time-changes of unipotent flows on finite volume quotients of semisimple linear groups, generalising previous work by Ratner on time-changes of horocycle flows. Any measur…
math.DS2024
Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows
Livio Flaminio, Davide Ravotti
We consider Abelian covers of compact hyperbolic surfaces. We establish an asymptotic expansion of the correlations for the horocycle flow on -covers, thus proving a…